1. Field of the Invention
This invention generally pertains to the prediction of wind-driven setup or setdown on the continental shelf, and mor specifically to an algorithm for the prediction of wind-driven setup or setdown utilizing information gathered from satellite observation of the waters surrounding the coastal region.
2. Description of the Related Art
One of the principle driving forces on continental shelf circulation is surface wind stress. The wind stress during extreme events can cause a sea level rise (setup) or sea level drop (setdown) in coastal areas. One approach to providing a useful wind setup or setdown forecast is through statistical use if in situ measurements. By relating the observed sea level changes to the observed wind stress forcing, it is possible to generate the expected relation between the two. In order to generate the requires statistical relations in terms of a linear transfer response function, a long time period climatologies of both sea level and wind stress are required. However, there are few in situ observations of sea level that cover a sufficiently long time period to be of use in this procedure.
Examining the sea surface response to wind forcing leads to an understanding of how wind stress may force subsuracce currents and control mixing across the shelf break.
Altimeter-measured sea surface height (SSH) variations collected by a satellite, such as the TOPEX/POSEIDON (T/P), presents an excellent opportunity to observe the behavior of the ocean in the continential shelf region. The altimeter data implications are well understood in the open ocean, and this has been exploited in many studies to examine ocean circulation physics. The lack of altimeter data applications to shallow water regions such as the continential shelf stems mainly from the lack of sufficient temporal sampling. Examining the evolution of the SSH response to a single winter wind burst or the passage of an individual typhoon or hurricane is impossible with a space-borne instrument that may sample only one ground track in the region of interest during a given day.
However, undersampled signals are not hopelessly lost. In particular, the dynamics of a linear deterministic process may be determined from observations of the forcing and response. For the case of wind-driven SSH, knowledge of the time of the measurements and the simultaneous forcing function allows the analysis to be made through a statistical approach. Another example is diurnal and semidiurnal tides which are aliased by the altimeter sampling scheme. In spite of the undersampling, much work has been done to use altimeter data to estimate tides both globally in deep water and locally in shallow water.
Wind stress forcing is a stochastic process. For each SSH measurement the wind forcing must be measured at the same time. Wind stress products, such as those of the Navy Operational Global Atmospheric rediction System (NOGAPS), provide fields at 12-hour intervals or less, which is sufficient temporal sampling to measure wind forcing events. The wind fields may be sampled at the altimeter measurement times, which allows determination of stochastic, or averaged, SSH response. If there are several observations of SSH and several simultaeous observations of the wind stress, the average SSH response can be calculated. The temporal sampling is inconsequential as long as a sufficient number of wind events and their responses are observed. In addition, by examining the time-lagged cross covariance of the SSH and wind stress, the response to the time-lagged wind stress and hence the stochastic temporal evolution of the SSH response may also be examined.
A significant problem in this process is the sample time difference between different altimeter ground tracks. The temporal difference (up to 5 days for T/P) implies that the satellite may have sampled a response to entirely different wind events along two different ground tracks. Thus the errors in the cross covariance between SSH and wind stress are more correlated along ground tracks than between different ground tracks. In the limit of an increasingly long time period data set, the points along each different ground track will be influenced by a sufficient number of events so that errors in the SSH to wind stress cross covariance will be small. For a data set of about 100, it is small enough that the response function for two ground tracks that are slightly different even at the same point in space. The effects on the fraction of SSH variability that may be explained are even larger. Two tracks at a crossover point may show identical response to wind forcing, but the calculated response may be able to explain much more variability along one ground track than the other because of the different events observed by the two time series.
Other methods for calculating the SSH response to wind stress include canonical correlation analysis (CCA) or principle estimator pattern (PEP) analysis. For these analyses the empirical orthogonal function (EOF) expansion of both variables (wind stress and SSH) is required. Studies of the altimeter data through extended EOF (EEOF) decompositions have been conducted to understand the annual and interannual variability. The EEOF decomposition requires gridding the altimeter data in space and time. However, for vartiations that are shorter than the satellite sampling period it is not possible to interpolate the data to a regular grid while maintaining the ocean variability of interest. Thus the EOF expansion of the altimeter SSH is not possible for this study. A numerical ocean model may also be used to produce the SSH response to wind forcing in both linear and nonlinear systems. However, numerical models are often hampered by the lack of accurate geometry data for coastline positions and bathymetry. Parameterization of processes such as boundary conditions, friction, and turblence also present challenges. Thus it is useful to examine the SSH response from a purely observational point of view.